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    <p>2021/10/21 更新了高位截肢</p>
<h1 id="高新区比赛"><a class="anchor" href="#高新区比赛">#</a> 高新区比赛</h1>
<p>V^3<br />
 好像是一个 2017 年的题改的<br />
 cnhongke {bf7e02677b4faab7808d1580fd5bb}<br />
 也可以手动爆破<br />
就是按照对应关系<br />
然后逐位加密<br />
你会发现到第六个就开始变成对称了<br />
所以手动跑 5 次就出结果了<br />
 exp 都多余了<br />
附上 exp:</p>
<figure class="highlight python"><figcaption data-lang="python"></figcaption><table><tr><td data-num="1"></td><td><pre>s <span class="token operator">=</span> <span class="token string">"ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789abcdefghijklmnopqrstuvwxyz_&#123;&#125;"</span></pre></td></tr><tr><td data-num="2"></td><td><pre></pre></td></tr><tr><td data-num="3"></td><td><pre></pre></td></tr><tr><td data-num="4"></td><td><pre><span class="token keyword">def</span> <span class="token function">_l</span><span class="token punctuation">(</span>idx<span class="token punctuation">,</span> s<span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="5"></td><td><pre>    <span class="token keyword">return</span> s<span class="token punctuation">[</span>idx<span class="token punctuation">:</span><span class="token punctuation">]</span> <span class="token operator">+</span> s<span class="token punctuation">[</span><span class="token punctuation">:</span>idx<span class="token punctuation">]</span></pre></td></tr><tr><td data-num="6"></td><td><pre></pre></td></tr><tr><td data-num="7"></td><td><pre></pre></td></tr><tr><td data-num="8"></td><td><pre><span class="token keyword">def</span> <span class="token function">decrypt</span><span class="token punctuation">(</span>ct<span class="token punctuation">,</span> k1<span class="token punctuation">,</span> k2<span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="9"></td><td><pre>    s <span class="token operator">=</span> <span class="token string">"ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789abcdefghijklmnopqrstuvwxyz_&#123;&#125;"</span></pre></td></tr><tr><td data-num="10"></td><td><pre>    t <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">[</span>_l<span class="token punctuation">(</span><span class="token punctuation">(</span>i <span class="token operator">+</span> j<span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">,</span> s<span class="token punctuation">)</span> <span class="token keyword">for</span> j <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="11"></td><td><pre>    i1 <span class="token operator">=</span> <span class="token number">0</span></pre></td></tr><tr><td data-num="12"></td><td><pre>    i2 <span class="token operator">=</span> <span class="token number">0</span></pre></td></tr><tr><td data-num="13"></td><td><pre>    decrypted <span class="token operator">=</span> <span class="token string">""</span></pre></td></tr><tr><td data-num="14"></td><td><pre>    <span class="token keyword">for</span> a <span class="token keyword">in</span> ct<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="15"></td><td><pre>        <span class="token keyword">for</span> c <span class="token keyword">in</span> s<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="16"></td><td><pre>            <span class="token keyword">if</span> t<span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>c<span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>k1<span class="token punctuation">[</span>i1<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>k2<span class="token punctuation">[</span>i2<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span> <span class="token operator">==</span> a<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="17"></td><td><pre>                decrypted <span class="token operator">+=</span> c</pre></td></tr><tr><td data-num="18"></td><td><pre>                <span class="token keyword">break</span></pre></td></tr><tr><td data-num="19"></td><td><pre>        i1 <span class="token operator">=</span> <span class="token punctuation">(</span>i1 <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>k1<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="20"></td><td><pre>        i2 <span class="token operator">=</span> <span class="token punctuation">(</span>i2 <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>k2<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="21"></td><td><pre>    <span class="token keyword">return</span> decrypted</pre></td></tr><tr><td data-num="22"></td><td><pre></pre></td></tr><tr><td data-num="23"></td><td><pre></pre></td></tr><tr><td data-num="24"></td><td><pre><span class="token keyword">def</span> <span class="token function">encrypt</span><span class="token punctuation">(</span>p<span class="token punctuation">,</span> k1<span class="token punctuation">,</span> k2<span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="25"></td><td><pre>    t <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">[</span>_l<span class="token punctuation">(</span><span class="token punctuation">(</span>i <span class="token operator">+</span> j<span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">,</span> s<span class="token punctuation">)</span> <span class="token keyword">for</span> j <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token builtin">len</span><span class="token punctuation">(</span>s<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="26"></td><td><pre>    i1 <span class="token operator">=</span> <span class="token number">0</span></pre></td></tr><tr><td data-num="27"></td><td><pre>    i2 <span class="token operator">=</span> <span class="token number">0</span></pre></td></tr><tr><td data-num="28"></td><td><pre>    c <span class="token operator">=</span> <span class="token string">""</span></pre></td></tr><tr><td data-num="29"></td><td><pre>    <span class="token keyword">for</span> a <span class="token keyword">in</span> p<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="30"></td><td><pre>        c <span class="token operator">+=</span> t<span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>k1<span class="token punctuation">[</span>i1<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">[</span>s<span class="token punctuation">.</span>find<span class="token punctuation">(</span>k2<span class="token punctuation">[</span>i2<span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="31"></td><td><pre>        i1 <span class="token operator">=</span> <span class="token punctuation">(</span>i1 <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>k1<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="32"></td><td><pre>        i2 <span class="token operator">=</span> <span class="token punctuation">(</span>i2 <span class="token operator">+</span> <span class="token number">1</span><span class="token punctuation">)</span> <span class="token operator">%</span> <span class="token builtin">len</span><span class="token punctuation">(</span>k2<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="33"></td><td><pre>    <span class="token keyword">return</span> c</pre></td></tr><tr><td data-num="34"></td><td><pre></pre></td></tr><tr><td data-num="35"></td><td><pre></pre></td></tr><tr><td data-num="36"></td><td><pre><span class="token keyword">def</span> <span class="token function">recover_key</span><span class="token punctuation">(</span>known_prefix<span class="token punctuation">,</span> ciphertex<span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="37"></td><td><pre>    final_key <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token string">'*'</span><span class="token punctuation">]</span> <span class="token operator">*</span> <span class="token number">14</span></pre></td></tr><tr><td data-num="38"></td><td><pre>    <span class="token keyword">for</span> pos <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="39"></td><td><pre>        <span class="token keyword">for</span> c <span class="token keyword">in</span> s<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="40"></td><td><pre>            partial_candidate_key <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token string">'*'</span><span class="token punctuation">]</span> <span class="token operator">*</span> <span class="token number">14</span></pre></td></tr><tr><td data-num="41"></td><td><pre>            partial_candidate_key<span class="token punctuation">[</span>pos<span class="token punctuation">]</span> <span class="token operator">=</span> c</pre></td></tr><tr><td data-num="42"></td><td><pre>            partial_candidate_key<span class="token punctuation">[</span><span class="token number">13</span> <span class="token operator">-</span> pos<span class="token punctuation">]</span> <span class="token operator">=</span> c</pre></td></tr><tr><td data-num="43"></td><td><pre>            key <span class="token operator">=</span> <span class="token string">""</span><span class="token punctuation">.</span>join<span class="token punctuation">(</span>partial_candidate_key<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="44"></td><td><pre>            res <span class="token operator">=</span> encrypt<span class="token punctuation">(</span>known_prefix<span class="token punctuation">,</span> key<span class="token punctuation">,</span> key<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">:</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="45"></td><td><pre>            <span class="token keyword">if</span> res<span class="token punctuation">[</span>pos<span class="token punctuation">]</span> <span class="token operator">==</span> ciphertex<span class="token punctuation">[</span>pos<span class="token punctuation">]</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="46"></td><td><pre>                final_key<span class="token punctuation">[</span>pos<span class="token punctuation">]</span> <span class="token operator">=</span> c</pre></td></tr><tr><td data-num="47"></td><td><pre>                final_key<span class="token punctuation">[</span><span class="token number">13</span> <span class="token operator">-</span> pos<span class="token punctuation">]</span> <span class="token operator">=</span> c</pre></td></tr><tr><td data-num="48"></td><td><pre>                <span class="token keyword">print</span> <span class="token string">""</span><span class="token punctuation">.</span>join<span class="token punctuation">(</span>final_key<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="49"></td><td><pre>    <span class="token keyword">return</span> <span class="token string">""</span><span class="token punctuation">.</span>join<span class="token punctuation">(</span>final_key<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="50"></td><td><pre></pre></td></tr><tr><td data-num="51"></td><td><pre></pre></td></tr><tr><td data-num="52"></td><td><pre><span class="token keyword">def</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="53"></td><td><pre>    ciphertext <span class="token operator">=</span> <span class="token string">"POR4dnyTLHBfwbxAAZhe&#125;&#125;ocZR3Cxcftw9"</span></pre></td></tr><tr><td data-num="54"></td><td><pre>    key <span class="token operator">=</span> recover_key<span class="token punctuation">(</span><span class="token string">"SECCON&#123;"</span><span class="token punctuation">,</span> ciphertext<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="55"></td><td><pre>    flag <span class="token operator">=</span> decrypt<span class="token punctuation">(</span>ciphertext<span class="token punctuation">,</span> key<span class="token punctuation">,</span> key<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">:</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="56"></td><td><pre>    <span class="token keyword">print</span><span class="token punctuation">(</span>flag<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="57"></td><td><pre></pre></td></tr><tr><td data-num="58"></td><td><pre></pre></td></tr><tr><td data-num="59"></td><td><pre>main<span class="token punctuation">(</span><span class="token punctuation">)</span></pre></td></tr></table></figure><h1 id="rsarepeat"><a class="anchor" href="#rsarepeat">#</a> RSArepeat</h1>
<p>这题好像也有层一样的，比赛真 lao<br />
 给出加密脚本</p>
<pre><code>#!/usr/bin/env python
# -*- coding: utf-8 -*-
from Crypto.Util.number import *
import gmpy2
import os
from secret import flag


p = gmpy2.next_prime(bytes_to_long(os.urandom(32) * 10))
q = getPrime(2048)
n = p * q
m = bytes_to_long(flag)
e = 65537
c = pow(m, e, n)
print 'n = ' + str(n)
print 'c = ' + str(c)


运行结果输出
# n = 9120210412817098868567410854637632250220555881403526554620639158581419400118706476426462580532569560128403528542849222604236640862674516611277130361890497616002043535833874824203278779255224103895976559478230598208736638548838369515266506758788653023380759388265524679357661867344583727639009050611035809615332415345615636794183389139631751072725812173232153921977529854299720035907475080123728133963132357285009229616899363413864250134103133772163607484794238528972871955212167583918722247406108717508117668301570190879613631465451744135100528987401664293214977426648232669628002711796584477405954390921585168542545024508132280795239187047607902042772074354512983547626983416047058674495234725402709185065533866399101327869049927071762987405052014360342557346201760417195526717659432120957024932822171629034785982161149134423193624715061013742839402782240625571812632970088905336230003285927069650264756078977556405903281928093668669291639199556779542688708405151017597677182338101624350346890556571828242761503472862589187188272783083175514693346986425145048900560704517281059296515380916946885637766528669652741939121435925118622627340581156923111326642804173809225000120356084999577920000481451709828075752253192537628742219663830938886966680564258836058435847445136469870523064012091603727249413340707659477419033271750976011384443208371660411376327908639483034074911057106131325663
# c = 7068462753085070298092306006815948822917293261569147262935876173777154611330212172780298815871946045639185357656186163809499649889823797927617022879328397754544340874952687572138224768719999154448738757631265317915591819395360957051438805269461772096089208044993726972263528636921213722053915213474520713305628933165329554039041526341429811011879399124487420973883220496337343697082485151325947637134492168684404895651666064423117891350949942888278577264641878267652440305311472437072576068073588628794693349303196170011208043072754814062079404857657352761995684725014730958374555123902870761944058212939416619872746207245705213743023048901892977114871581000445118225605980711967279184600832881914000747237143653411293658641093111449235793736446421524719927367452081557329271167988711131750096910582920748875147684842547191116046110455610485921697703084407073334158845880179092914138111196153821093666870713318435216431977100255451151613217255214311447270315317924828002186873831048826117341746203538919869858723643158591679168166815433400943179342639989830429265410316662281946735133048179580170395697284908451588172527612828357594205617900793644449780703541620423822874332895281227408264377675840472406248296158342659308845264164232068007825845287325024564804783116616695927303806931940737550484802677095488750998780934178991718038605826623684585430755074719975767565185371149546480577

</code></pre>
<p><img data-src="/img/CRYPTO/gaoxinqu1.jpg" alt="avatar" /><br />
<img data-src="/img/CRYPTO/gaoxinqu2.jpg" alt="avatar" /></p>
<p>附上 exp:</p>
<figure class="highlight python"><figcaption data-lang="python"></figcaption><table><tr><td data-num="1"></td><td><pre><span class="token comment">#!python2</span></pre></td></tr><tr><td data-num="2"></td><td><pre><span class="token comment"># -*- coding: utf-8 -*-</span></pre></td></tr><tr><td data-num="3"></td><td><pre><span class="token comment"># @FileName: tt.py</span></pre></td></tr><tr><td data-num="4"></td><td><pre><span class="token keyword">from</span> Crypto<span class="token punctuation">.</span>Util<span class="token punctuation">.</span>number <span class="token keyword">import</span> <span class="token operator">*</span></pre></td></tr><tr><td data-num="5"></td><td><pre>n <span class="token operator">=</span> <span class="token number">5723803231105438067621879312731287221934357097569268166420520040038029065761152553810494005387890506233399584147246538077002208499639437803910245817342952372458171365752480055753844375305610474395282822742943102904320741363812652705261682747336617279332644951905181705937705454682585492345619282271549850191266841799115355201225481894665469006243078988838181049476985523095183211083306888898330855716843411424493132244378006508444594329543929521327878717314543259397842391141445238073295183064204038877358053346160904246766744058035260700906186262991418344028036927076898224775513313992135215728859733003918328707361999295628679324987941544108516966440200369017207031702010292125100166826894159577761774445100777211415862293977599736904535299914065534202980062824965765410888738320552504576390375348702993646394541895827629891842496139670703262245710062952138603857926812293927639685763696276258111848707179034963859209200388611940617575570592428927246122690317085150458638646993030523460057013506016279214894927343923461607646478524983809407592464446504390449868558006440884166283766345457345779137687215125369153544179042534504852071842244821976629524307628462619103368289645015324069375881393414723379127777033799199839545069927720992165031027897683055528657202955467661225465098604530590852960596629917086084805687598732530884961789893076147057895925224397540225533098516204541840889</span></pre></td></tr><tr><td data-num="6"></td><td><pre>t<span class="token operator">=</span>bytes_to_long<span class="token punctuation">(</span><span class="token punctuation">(</span><span class="token string">'\x00'</span><span class="token operator">*</span><span class="token number">31</span><span class="token operator">+</span><span class="token string">'\x01'</span><span class="token punctuation">)</span><span class="token operator">*</span><span class="token number">10</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="7"></td><td><pre><span class="token comment">#print t</span></pre></td></tr><tr><td data-num="8"></td><td><pre>K <span class="token operator">=</span> Zmod<span class="token punctuation">(</span>n<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="9"></td><td><pre>P<span class="token punctuation">.</span><span class="token operator">&lt;</span>x<span class="token operator">></span> <span class="token operator">=</span> PolynomialRing<span class="token punctuation">(</span>K<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="10"></td><td><pre><span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">100000</span><span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="11"></td><td><pre>    r <span class="token operator">=</span><span class="token punctuation">(</span>x <span class="token operator">*</span>t <span class="token operator">+</span>i<span class="token punctuation">)</span><span class="token punctuation">.</span>monic<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span>small_roots<span class="token punctuation">(</span>beta<span class="token operator">=</span><span class="token number">0.45</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="12"></td><td><pre>    <span class="token keyword">if</span> r<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="13"></td><td><pre>        <span class="token keyword">print</span> i<span class="token punctuation">,</span>r</pre></td></tr></table></figure><h1 id="维吉尼亚"><a class="anchor" href="#维吉尼亚">#</a> 维吉尼亚</h1>
<p>听名字就知道</p>
<pre><code>Vvr Ifnvaus Bdwokv Gbtrzsa Vkqgofntja rrlznxk eflvkozjcdue rs “mzg oez ff pjkhvtx ok kqzioeg vgfsf.” Zyil au vvykokaeoyrp avuwfnzv, bnl fcry eom ucdgaie mzg qhxiegl dfrguta gh huk wixdf ce oks ijggrtk-dtq uqvketbxkq sulnwsvwbtj. Taw fssoeimaqb sutulwu gbrvlr gp huk towwu hugk htng prke ulwf tbx teglwfvkj th wpoorv sxutsg ifmfmpwpgkihf. Dig iiyilquegghr fqknjryl wpqbsgalkgg zath fgts gnrn mzkg: vz uetdu kvzy mxujoaojml xqf rtjukapu vtkezjkhl, zvcafkehkj fhj glpnrnzapu fktrxl msly, grhlqqbrj fhj cignvnmaeogoeg nkgff, kcevltcaot anuvwbtj agv gzrikihfu, rvmzttd eofn, rnw eqfr. Cztagwh nzkefhvwam ko ijqjvjv a vgodykke vzcfnikekabogofn, pw ychru stq vvnz dowwtb pxppmgifnvyy bfxcybvs mzg ggauy hx oognvmtlkqnr kevzpwdavs ygt grilrbfi rvmzttd kbsuimtlkca, ypsmwog, ntu dbkvfvhltxv eczvlttlkcay rgtapgg guvxjuoeorl tlvopqj. CgZqbtQv&#123;3ayuc4r633096o2737&#125;
</code></pre>
<p>直接维吉尼亚枚举</p>
<pre><code>The Concise Oxford English Dictionary defines cryptography as “the art of writing or solving codes.” This is historically accurate, but does not capture the current breadth of the field or its present-day scientific foundations. The definition focuses solely on the codes that have been used for centuries to enable secret communication. But cryptography nowadays encompasses much more than this: it deals with mechanisms for ensuring integrity, techniques for exchanging secret keys, protocols for authenticating users, electronic auctions and elections, digital cash, and more. Without attempting to provide a complete characterization, we would say that modern cryptography involves the study of mathematical techniques for securing digital information, systems, and distributed computations against adversarial attacks. CnHongKe&#123;3afca4d633096b2737&#125;
</code></pre>
<p>真 lao</p>
<h1 id="高位截肢"><a class="anchor" href="#高位截肢">#</a> 高位截肢</h1>
<p>題目源代碼</p>
<figure class="highlight python"><figcaption data-lang="python"></figcaption><table><tr><td data-num="1"></td><td><pre><span class="token keyword">from</span> random <span class="token keyword">import</span> randint</pre></td></tr><tr><td data-num="2"></td><td><pre><span class="token keyword">from</span> gmpy2 <span class="token keyword">import</span> <span class="token operator">*</span></pre></td></tr><tr><td data-num="3"></td><td><pre><span class="token keyword">from</span> Crypto<span class="token punctuation">.</span>Util<span class="token punctuation">.</span>number <span class="token keyword">import</span> <span class="token operator">*</span></pre></td></tr><tr><td data-num="4"></td><td><pre></pre></td></tr><tr><td data-num="5"></td><td><pre></pre></td></tr><tr><td data-num="6"></td><td><pre>m <span class="token operator">=</span> bytes_to_long<span class="token punctuation">(</span><span class="token string">b'flag&#123;********************************&#125;'</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="7"></td><td><pre></pre></td></tr><tr><td data-num="8"></td><td><pre><span class="token keyword">def</span> <span class="token function">getprime</span><span class="token punctuation">(</span>bits<span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="9"></td><td><pre>    <span class="token keyword">while</span> <span class="token number">1</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="10"></td><td><pre>        n <span class="token operator">=</span> <span class="token number">1</span></pre></td></tr><tr><td data-num="11"></td><td><pre>        <span class="token keyword">while</span> n<span class="token punctuation">.</span>bit_length<span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">&lt;</span> bits<span class="token punctuation">:</span></pre></td></tr><tr><td data-num="12"></td><td><pre>            n <span class="token operator">*=</span> next_prime<span class="token punctuation">(</span>randint<span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token number">1000</span><span class="token punctuation">)</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="13"></td><td><pre>        <span class="token keyword">if</span> isPrime<span class="token punctuation">(</span>n <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">:</span></pre></td></tr><tr><td data-num="14"></td><td><pre>            <span class="token keyword">return</span> n <span class="token operator">-</span> <span class="token number">1</span></pre></td></tr><tr><td data-num="15"></td><td><pre></pre></td></tr><tr><td data-num="16"></td><td><pre>p <span class="token operator">=</span> getprime<span class="token punctuation">(</span><span class="token number">512</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="17"></td><td><pre>q <span class="token operator">=</span> getprime<span class="token punctuation">(</span><span class="token number">512</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="18"></td><td><pre>n <span class="token operator">=</span> p<span class="token operator">*</span>q</pre></td></tr><tr><td data-num="19"></td><td><pre>e <span class="token operator">=</span> <span class="token number">65537</span></pre></td></tr><tr><td data-num="20"></td><td><pre>d <span class="token operator">=</span> invert<span class="token punctuation">(</span>e<span class="token punctuation">,</span><span class="token punctuation">(</span>p<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">*</span><span class="token punctuation">(</span>q<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="21"></td><td><pre>c <span class="token operator">=</span> <span class="token builtin">pow</span><span class="token punctuation">(</span>m<span class="token punctuation">,</span>e<span class="token punctuation">,</span>n<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="22"></td><td><pre></pre></td></tr><tr><td data-num="23"></td><td><pre>res <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="24"></td><td><pre>mod <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="25"></td><td><pre><span class="token punctuation">[</span>mod<span class="token punctuation">.</span>append<span class="token punctuation">(</span>getprime<span class="token punctuation">(</span><span class="token number">128</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">12</span><span class="token punctuation">)</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="26"></td><td><pre><span class="token punctuation">[</span>res<span class="token punctuation">.</span>append<span class="token punctuation">(</span>c<span class="token operator">%</span>mod<span class="token punctuation">[</span>i<span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token keyword">for</span> i <span class="token keyword">in</span> <span class="token builtin">range</span><span class="token punctuation">(</span><span class="token number">12</span><span class="token punctuation">)</span><span class="token punctuation">]</span></pre></td></tr><tr><td data-num="27"></td><td><pre><span class="token keyword">print</span><span class="token punctuation">(</span>n<span class="token punctuation">,</span><span class="token punctuation">(</span>p<span class="token operator">>></span><span class="token number">128</span><span class="token punctuation">)</span><span class="token operator">&lt;&lt;</span><span class="token number">128</span><span class="token punctuation">)</span><span class="token punctuation">,</span>mod<span class="token punctuation">,</span>res<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="28"></td><td><pre></pre></td></tr><tr><td data-num="29"></td><td><pre><span class="token triple-quoted-string string">'''</pre></td></tr><tr><td data-num="30"></td><td><pre>output:</pre></td></tr><tr><td data-num="31"></td><td><pre>3216831712236484919804716473942409526434016529181790011140718891645020999952523287950679312500771653918738887189899203815116997399422419456666136527466294225647700744715569996552708989626431982330367733125015062070399091789218760399060531383324158096784030850407432126491091299460659042468401054516052600467997</pre></td></tr><tr><td data-num="32"></td><td><pre>36691536769373164488130311421517753226870999465362409179446664596323017708216823951466573340643687346264018616414288774195411449434676147898363218552160256</pre></td></tr><tr><td data-num="33"></td><td><pre>[127358722814661886628344839530462144916373, 1569005233424413714924223862235964763229, 15953826944429720811716497916877126603181, 22667750449179799152236917772041505492557, 7259500259309895932387328648172298540473, 1216723397014858024629084355784570444737, 5803969258694833349275399163572927306963, 2847514965593473340352693322675908465517, 55965603506094486681210827499140188004581, 3758825246939161175629619499256754206153, 9865309015695677187200661453839724337633, 1985189335531812324455545509044214546841)]</pre></td></tr><tr><td data-num="34"></td><td><pre>[17514122934988110165886587218707943859589, 828023569353871016099054873610645592579, 3834965867062595899595546144451189629655, 5083410101797762407471893731877939884166, 6199590917760184276466050254032811548454, 208337506454727094683323122852921121527, 5210709327454808237359999225611588134922, 239093795148407379152016295908193630983, 29793049900271876372064873251244672365333, 1641943491807405218384351799880631607416, 1685895805013787734204509484411577153108, 1511298522529374764380482522275435302730)]</pre></td></tr><tr><td data-num="35"></td><td><pre>'''</span></pre></td></tr></table></figure><p>高位攻擊恢復 p+crt<br />
 給大家推薦幾個高位攻擊回復 p 的 blog<br />
<span class="exturl" data-url="aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2xvc3RuZXJ2L2FydGljbGUvZGV0YWlscy8xMDYwMDkxMjc=">https://blog.csdn.net/lostnerv/article/details/106009127</span></p>
<p><span class="exturl" data-url="aHR0cHM6Ly93d3cuamlhbnNodS5jb20vcC9lNDA3YmUzOWEyMmI=">https://www.jianshu.com/p/e407be39a22b</span></p>
<p>上脚本</p>
<figure class="highlight python"><figcaption data-lang="python"></figcaption><table><tr><td data-num="1"></td><td><pre><span class="token keyword">from</span> Crypto<span class="token punctuation">.</span>Util<span class="token punctuation">.</span>number <span class="token keyword">import</span> <span class="token operator">*</span></pre></td></tr><tr><td data-num="2"></td><td><pre><span class="token keyword">from</span> sympy <span class="token keyword">import</span> <span class="token operator">*</span></pre></td></tr><tr><td data-num="3"></td><td><pre></pre></td></tr><tr><td data-num="4"></td><td><pre><span class="token comment">#sage</span></pre></td></tr><tr><td data-num="5"></td><td><pre><span class="token triple-quoted-string string">'''</pre></td></tr><tr><td data-num="6"></td><td><pre>#高位p</pre></td></tr><tr><td data-num="7"></td><td><pre>e = 65537</pre></td></tr><tr><td data-num="8"></td><td><pre>n = 3216831712236484919804716473942409526434016529181790011140718891645020999952523287950679312500771653918738887189899203815116997399422419456666136527466294225647700744715569996552708989626431982330367733125015062070399091789218760399060531383324158096784030850407432126491091299460659042468401054516052600467997</pre></td></tr><tr><td data-num="9"></td><td><pre>pbar = 36691536769373164488130311421517753226870999465362409179446664596323017708216823951466573340643687346264018616414289061014410434943387973225734363385787789</pre></td></tr><tr><td data-num="10"></td><td><pre>kbits = 128</pre></td></tr><tr><td data-num="11"></td><td><pre>print("upper %d bits (of %d bits) is given" % (pbar.nbits()-kbits, pbar.nbits()))</pre></td></tr><tr><td data-num="12"></td><td><pre>PR.&lt;x> = PolynomialRing(Zmod(n))</pre></td></tr><tr><td data-num="13"></td><td><pre>f = x + pbar</pre></td></tr><tr><td data-num="14"></td><td><pre>x0 = f.small_roots(X=2^kbits, beta=0.4)[0]  # find root &lt; 2^kbits with factor >= n^0.4</pre></td></tr><tr><td data-num="15"></td><td><pre>p = x0 + pbar</pre></td></tr><tr><td data-num="16"></td><td><pre>print("p:", p)</pre></td></tr><tr><td data-num="17"></td><td><pre>#crt求c</pre></td></tr><tr><td data-num="18"></td><td><pre>crt([17514122934988110165886587218707943859589, 828023569353871016099054873610645592579, 3834965867062595899595546144451189629655, 5083410101797762407471893731877939884166, 6199590917760184276466050254032811548454, 208337506454727094683323122852921121527, 5210709327454808237359999225611588134922, 239093795148407379152016295908193630983, 29793049900271876372064873251244672365333, 1641943491807405218384351799880631607416, 1685895805013787734204509484411577153108, 1511298522529374764380482522275435302730],[127358722814661886628344839530462144916373, 1569005233424413714924223862235964763229, 15953826944429720811716497916877126603181, 22667750449179799152236917772041505492557, 7259500259309895932387328648172298540473, 1216723397014858024629084355784570444737, 5803969258694833349275399163572927306963, 2847514965593473340352693322675908465517, 55965603506094486681210827499140188004581, 3758825246939161175629619499256754206153, 9865309015695677187200661453839724337633, 1985189335531812324455545509044214546841])</pre></td></tr><tr><td data-num="19"></td><td><pre>'''</span></pre></td></tr><tr><td data-num="20"></td><td><pre>c <span class="token operator">=</span> <span class="token number">1077233712188252453962763215420078090384941182152999954278038468778840824135535740613334922110769959923025621861732351020130627648669752220543773285487384058164614139587422610914396593954389899763791857297268825420364912075493471765126196898848111738107851858382589951634394904231520912326280908229934082041817</span></pre></td></tr><tr><td data-num="21"></td><td><pre>n <span class="token operator">=</span> <span class="token number">3216831712236484919804716473942409526434016529181790011140718891645020999952523287950679312500771653918738887189899203815116997399422419456666136527466294225647700744715569996552708989626431982330367733125015062070399091789218760399060531383324158096784030850407432126491091299460659042468401054516052600467997</span></pre></td></tr><tr><td data-num="22"></td><td><pre>p <span class="token operator">=</span> <span class="token number">36691536769373164488130311421517753226870999465362409179446664596323017708216823951466573340643687346264018616414289061014410434943387973225734363385787789</span></pre></td></tr><tr><td data-num="23"></td><td><pre>q <span class="token operator">=</span> n<span class="token operator">//</span>p</pre></td></tr><tr><td data-num="24"></td><td><pre>e <span class="token operator">=</span> <span class="token number">65537</span></pre></td></tr><tr><td data-num="25"></td><td><pre>d <span class="token operator">=</span> invert<span class="token punctuation">(</span>e<span class="token punctuation">,</span> <span class="token punctuation">(</span>p<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token operator">*</span><span class="token punctuation">(</span>q<span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">)</span></pre></td></tr><tr><td data-num="26"></td><td><pre>m <span class="token operator">=</span> <span class="token builtin">pow</span><span class="token punctuation">(</span>c<span class="token punctuation">,</span> <span class="token builtin">int</span><span class="token punctuation">(</span>d<span class="token punctuation">)</span><span class="token punctuation">,</span> n<span class="token punctuation">)</span></pre></td></tr><tr><td data-num="27"></td><td><pre><span class="token keyword">print</span><span class="token punctuation">(</span>long_to_bytes<span class="token punctuation">(</span>m<span class="token punctuation">)</span><span class="token punctuation">)</span></pre></td></tr></table></figure><p>flag{5bb5e0a9d48f44a3770253875f263810}<br />
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